Metric properties of Sierpiński graphsZemljič, Sara Sabrina (Avtor) Klavžar, Sandi (Mentor) Sierpiński graphSierpiński-type graphdistancealmost-extreme vertexdistance of a vertexmetric dimensionswitching Tower of Hanoicanonical metric representationHamming dimensioninduced embeddingIn this thesis we study the metric properties of Sierpiński graphs. Sierpiński graphs form a two-parametric family of graphs similar to Hanoi graphs that originate in the Tower of Hanoi puzzle. Sierpiński graphs can be found in various areas of mathematics and elsewhere. First we introduce the family of Sierpiński graphs and their variants. These families have been known under various names, and sometimes vice versa - different graphs under the same name. We therefore standardize their notations and names to avoid confusion in the future. Next we summarize what has already been studied on Sierpiński graphs. One chapter of the thesis is completely devoted to metric properties of Sierpiński graphs, where we first list known related results, in particular we state the distance lemma and the theorem about the distance between arbitrary two vertices. Since this distance is expressed with a minimum, we give improved results on distances in Sierpiński graphs for almost-extreme vertices. Namely, the distance between an arbitrary vertex and an almost-extreme vertex in a Sierpiński graph can be expressed with a closed formula. We conclude this part with determining the metric dimension of Sierpiński graphs. To better understand the structure of Sierpiński graphs we study various embeddings, beginning with the embeddings into Hanoi graphs. We also determine the canonical metric representation and induced embeddings. For the latter type of embeddings, we introduce the Hamming dimension and bound it for Sierpiński graphs. We conclude with some open problems.[S. S. Zemljič]20142017-09-22 02:53:48Doktorsko delo/naloga95854UDK: 519.17(043.3)COBISS_ID: 17047129sl